Hilfer and Hadamard functional random fractional differential inclusions

Saïd Abbas; Mouffak Benchohra; Jamal-Eddine Lazreg; Gaston M. N‘Guérékata

doi:10.4067/S0719-06462017000100002

Authors

Saïd Abbas Laboratory of Mathematics, University of Saïda, P.O. Box 138, Saïda 20000, Algeria
Mouffak Benchohra Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb`es 22000, Algeria.
Jamal-Eddine Lazreg Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abb`es 22000, Algeria.
Gaston M. N‘Guérékata Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA.

DOI:

https://doi.org/10.4067/S0719-06462017000100002

Keywords:

Functional Random differential inclusion, left-sided Riemann-Liouville integral of fractional order, left-sided Hadamard integral of fractional order, Hilfer fractional derivative, convex, non-convex, Hilfer-Hadamard fractional derivative, existence, Ulam stability, random solution, fixed point

Abstract

This paper deals with some existence and Ulam stability results for some functional differential inclusions of Hilfer and Hilfer-Hadamard type with convex and non-convex right hand side. We employ some multi-valued random fixed point theorems for the existence of random solutions. Next we prove that our problems are generalized Ulam-Hyers-Rassias stable.